CBSE CLASS 10 MATHEMATICS QUESTIONS AND ANSWERS PART 2

CLASS 10 CBSE MATHEMATICS QUESTIONS AND ANSWERS PART 2
ANSWERS ARE GIVEN IN YELLOW

1. OP is equal to the diameter of a circle with centre O and PA and PB are tangents. Prove that ABP is equilateral

Theorems used
Tangent is perpendicular to the radius at the point of contact.
Tangents drawn from an external point to a circle are equal in length.

Therefore ABP is equilateral.

2. Show that 571 is a prime number.

3. DE is parallel to BC. If (AD/DB) = (4/13) and AC=20.4 cm then find AE.

Basic Proportionality Theorem

If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

4. O is the centre of a circle. PQ is a chord and PT is a tangent at P which makes an angle of 50° with PQ. Find the angle POQ.

5. The sum of the first k terms of an AP is 3k^2-k. Find the first term and common difference.

6. The circumference of a circle exceeds the diameter by 16.8 cm. Find the radius of the circle.

7. Draw the graphs of x-y+1=0 and 3x+2y-12=0. Find the coordinates of the vertices of the triangle formed by these lines and the x-axis and shade the triangular region.

8. Verify whether A(3,0), B(6,4) andC(-1,3) are the vertices of a right angled triangle.

ABC is a right angled triangle as it satisfies Pythagoras theorem.

9. Simplify

10. Find the nature of roots of 2x²-3√2x+(9/4) = 0

The given equation has two equal and real roots.

11. If ɑ and β are the roots of 2x²-4x+5, then find the value of (1/ɑ²) + (1/β²)

12. If the TSA of a solid hemisphere is 462 cm², find its volume

13. If sin x = √3/2, find the value of 2cot²x -1

sinx = √3/2

So x = 60°

cot 60 = 1/√3

2cot²x - 1 = 2(1/√3)² - 1 = (2/3)-3= -1/3

14. Three bells toll at intervals of 9,12,15 minutes respectively. If they start tolling together, after what time will they toll together again?

15. AOB is a sector of angle 60 of a circle with centre O and radius 17 cm. If AP is perpendicular to OB and AP=15 cm, find the area of the shaded region.